Boundary control strategy is developed to analyze the vibration problem of the offshore ocean thermal energy conversion (OTEC) system as well as to constrain the bottom tension and top motion. To provide an accurate dynamic behavior for the OTEC system, this distributed parameter system is modeled and formulated with a governing equation and boundary conditions (PDE-ODEs model). Two robust adaptive boundary controllers are designed and disposed at the endpoints of the system, and the stability of the controlled system under unknown disturbances is achieved. After selecting the relevant parameters appropriately, the offset of the offshore OTEC system can be suppressed to equilibrium position. Finally, the effectiveness of the proposed control is illustrated by simulation.